An Analytical Method for Cylindrical Shells With Nozzles Due to Internal Pressure and External Loads—Part I: Theoretical Foundation

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Ming-De Xue ◽  
Qing-Hai Du ◽  
Keh-Chih Hwang ◽  
Zhi-Hai Xiang
Keyword(s):  
Analytical Solution ◽  
Internal Pressure ◽  
Stress Analysis ◽  
Pressure Vessel ◽  
Cylindrical Shells ◽  
Branch Pipe ◽  
Theoretical Solution ◽  
External Branch ◽  
Complex Valued ◽  
External Loads

An improved version of the analytical solutions by Xue, Hwang and co-workers (1991, “Some Results on Analytical Solution of Cylindrical Shells With Large Opening,” ASME J. Pressure Vessel Technol., 113, 297–307; 1991, “The Stress Analysis of Cylindrical Shells With Rigid Inclusions Having a Large Ratio of Radii,” SMiRT 11 Transactions F, F05/2, 85–90; 1995, “The Thin Theoretical Solution for Cylindrical Shells With Large Openings,” Acta Mech. Sin., 27(4), pp. 482–488; 1995, “Stresses at the Intersection of Two Cylindrical Shells,” Nucl. Eng. Des., 154, 231–238; 1996, “A Reinforcement Design Method Based on Analysis of Large Openings in Cylindrical Pressure Vessels,” ASME J. Pressure Vessel Technol., 118, 502–506; 1999, “Analytical Solution for Cylindrical Thin Shells With Normally Intersecting Nozzles Due to External Moments on the Ends of Shells,” Sci. China, Ser. A: Math., Phys., Astron., 42(3), 293–304; 2000, “Stress Analysis of Cylindrical Shells With Nozzles Due to External Run Pipe Moments,” J. Strain Anal. Eng. Des., 35, 159–170; 2004, “Analytical Solution of Two Intersecting Cylindrical Shells Subjected to Transverse Moment on Nozzle,” Int. J. Solids Struct., 41(24–25), 6949–6962; 2005, “A Thin Shell Theoretical Solution for Two Intersecting Cylindrical Shells Due to External Branch Pipe Moments,” ASME J. Pressure Vessel Technol., 127(4), 357–368; 2005, “Theoretical Stress Analysis of Two Intersecting Cylindrical Shells Subjected to External Loads Transmitted Through Branch Pipes,” Int. J. Solids Struct., 42, 3299–3319) for two normally intersecting cylindrical shells is presented, and the applicable ranges of the theoretical solutions are successfully extended from d/D≤0.8 and λ=d/(DT)1/2≤8 to d/D≤0.9 and λ≤12. The thin shell theoretical solution is obtained by solving a complex boundary value problem for a pair of fourth-order complex-valued partial differential equations (exact Morley equations (Morley, 1959, “An Improvement on Donnell’s Approximation for Thin Walled Circular Cylinders,” Q. J. Mech. Appl. Math. 12, 89–91; Simmonds, 1966, “A Set of Simple, Accurate Equations for Circular Cylindrical Elastic Shells,” Int. J. Solids Struct., 2, 525–541)) for the shell and the nozzle. The accuracy of results is improved by some additional terms to the expressions for resultant forces and moments in terms of complex-valued displacement-stress function. The theoretical stress concentration factors due to internal pressure obtained by the improved expressions are in agreement with previously published test results. The theoretical results discussed and presented herein are in sufficient agreement with those obtained from three dimensional finite element analyses for all the seven load cases, i.e., internal pressure and six external branch pipe load components involving three orthogonal forces and the respective three orthogonal moments.

A Universal Design Method Based on Analysis for Cylindrical Shells With Nozzles Due to Internal Pressure, External Forces and Moments: Part I

2009 ◽  
Author(s):  
Ming-De Xue ◽  
Qing-Hai Du ◽  
Keh-Chih Hwang ◽  
Zhi-Hai Xiang
Keyword(s):  
Internal Pressure ◽  
Design Method ◽  
Cylindrical Shells ◽  
Branch Pipe ◽  
External Branch ◽  
Complex Boundary ◽  
Stress Concentration Factors ◽  
Accuracy Of Results ◽  
External Forces ◽  
Complex Valued

An improved version is presented for analytical solution developed by the authors and the applicable ranges of the theoretical solutions for two normally intersecting cylindrical shells are successfully extended from d/D≤0.8 and λ=d/(DT)1/2≤8 up to d/D ≤0.9 and λ≤12. The thin shell theoretical solution is obtained by solving a complex boundary value problem for a pair of 4-th order complex-valued partial differential equations (exact Morley equations) for the shell and the nozzle. The accuracy of results is improved by some additional terms to the expressions for resultant forces and moments in terms of complex-valued displacement-stress function. The presented theoretical stress concentration factors due to pressure are in agreement with the test results in literatures. The presented theoretical results are in good agreement with those by 3-D finite element method for all the seven load cases, i.e., internal pressure and six external branch pipe load components involving axial tension, two kinds of transverse shear forces, longitudinal and circumferential bending and torsion moments.

A Stress Analysis Method for Cylindrical Shells With Nozzles Subjected to Internal Pressure, External Forces and Moments

2006 ◽  
Author(s):  
Ming-De Xue ◽  
Qing-Hai Du ◽  
Dong-Feng Li ◽  
Keh-Chih Hwang
Keyword(s):  
Internal Pressure ◽  
Stress Analysis ◽  
Thin Shell ◽  
Cylindrical Shells ◽  
Branch Pipe ◽  
Three Dimensional ◽  
Theoretical Solution ◽  
Analysis Method ◽  
External Forces ◽  
Three Dimensional Finite Element

An identical stress analysis method based on the thin shell theory is carried out for cylindrical shells with normally intersecting nozzles subjected to internal pressure and six kinds of external branch pipe loads involving axial tension, two kinds of transverse shear forces, longitudinal and circumferential bending and torsion moments. The thin shell theoretical solution is obtained based on the Morley equation instead of the Donnell shallow shell equation. The accurate continuity conditions at the intersecting curve, which is a complicated space curve, are adopted. The presented results are verified by three-dimensional finite element method (FEM). The theoretical solution can be applied to d/D ≤ 0.8, λ = d/DT ≤ 12 and d/D ≤ t/T ≤ 2 successfully. The solutions are in good agreement with WRC Bulletin 297 when diameter ratio is small. In the paper some typical design curves calculated by the theoretical solutions are presented and their applicable ranges are greatly expanded in comparison with current design methods.

A Thin Shell Theoretical Solution for Two Intersecting Cylindrical Shells Due to External Branch Pipe Moments

2004 ◽  
Author(s):  
M. D. Xue ◽  
D. F. Li ◽  
K. C. Hwang
Keyword(s):  
Thin Shell ◽  
Cylindrical Shells ◽  
Branch Pipe ◽  
Three Dimensional ◽  
Homogeneous Solution ◽  
Displacement Function ◽  
Theoretical Solution ◽  
External Branch ◽  
Particular Solution ◽  
Good Agreement

Two intersecting cylindrical shells subjected to internal pressure and external moment are of common occurrence in pressure vessel and piping industry. The highest stress intensity occurring in the vicinity of junction, which is a complex space curve when the diameter ratio d/D increases. As the new process of theoretical solution and design criteria research developed by the authors, the stress analysis based on the theory of thin shell is carried out for cylindrical shells with normally intersecting nozzles subjected to three kinds of external branch pipe moments. The thin shell theoretical solution for the main shell with cutout, on which a moment is applied, is obtained by superposing a particular solution on the homogeneous solution. The double trigonometric series solution of cylindrical shell subjected to arbitrary distributed normal and tangential forces based on Timoshenko equation is used for the particular solution and the Xue et al.’s solution, for the homogeneous solution based on the modified Morley equation instead of the Donnell shallow shell equation. The displacement function solution for the nozzle with a nonplanar end is obtained on the basis of the Goldenveizer equation instead of Timoshenko’s. The presented results are in good agreement with those obtained by experiments and by three-dimensional finite element method. The present analytical results are in good agreement with WRC Bulletin 297 when d/D is small. The theoretical solution can be applied to d/D ≤ 0.8, λ = d/DT ≤ 8 and d/D ≤ t/T ≤ 2 successfully.

A Thin Shell Theoretical Solution for Two Intersecting Cylindrical Shells Due to External Branch Pipe Moments

2005 ◽  
Vol 127 (4) ◽  
pp. 357-368 ◽  
Author(s):  
M. D. Xue ◽  
D. F. Li ◽  
K. C. Hwang
Keyword(s):  
Cylindrical Shells ◽  
Branch Pipe ◽  
Homogeneous Solution ◽  
Theoretical Solution ◽  
Intersection Curve ◽  
3D Fem ◽  
External Branch ◽  
Particular Solution ◽  
Shell Equation ◽  
Distributed Forces

A theoretical solution is presented for cylindrical shells with normally intersecting nozzles subjected to three kinds of external branch pipe moments. The improved double trigonometric series solution is used for the particular solution of main shell subjected to distributed forces, and the modified Morley equation instead of the Donnell shallow shell equation is used for the homogeneous solution of the shell with cutout. The Goldenveizer equation instead of Timoshenko’s is used for the nozzle with a nonplanar end. The accurate continuity conditions at the intersection curve are adopted instead of approximate ones. The presented results are in good agreement with those obtained by tests and by 3D FEM and with WRC Bulletin 297 when d∕D is small. The theoretical solution can be applied to d∕D⩽0.8, λ=d∕DT⩽8, and d∕D⩽t∕T⩽2 successfully.

Approximate Elastic Stresses in Pipe Junctions with Chamfer Corners

1981 ◽  
Vol 103 (1) ◽  
pp. 107-111
Author(s):  
D. P. Updike
Keyword(s):  
Internal Pressure ◽  
Stress Analysis ◽  
Elastic Stress ◽  
Branch Pipe ◽  
Optimum Size ◽  
Pressure Loading ◽  
Elastic Stresses ◽  
Rapid Calculation ◽  
Identical Diameter

Elastic stress analysis of a right angle tee branch pipe connection of two pipes of identical diameter and thickness connected through 45-deg chamfer corner sections is developed for internal pressure loading. Stresses in the crotch portion of the vessel are determined. These results are presented in the form of a table of factors useful for rapid calculation of approximate values of the peak stresses. The existence of a structurally optimum size of chamfer is demonstrated.

Elastic-Plastic Stress Analysis of Pressure Vessels

2012 ◽  
Author(s):  
Yang-chun Deng ◽  
Gang Chen
Keyword(s):  
Internal Pressure ◽  
Stress Analysis ◽  
Strain Hardening ◽  
Pressure Vessel ◽  
Plastic Instability ◽  
Pressure Vessels ◽  
Structural Deformation ◽  
Elastic Plastic ◽  
Thin Walled ◽  
Plastic Stress

To save material, the safety factor of pressure vessel design standards is gradually decreased from 5.0 to 2.4 in ASME Boiler and Pressure Vessel Codes. So the design methods of pressure vessel should be more rationalized. Considering effects of material strain hardening and non-linear structural deformation, the elastic-plastic stress analysis is the most suitable for pressure vessels design at present. This paper is based on elastic-plastic theory and considers material strain hardening and structural deformation effects. Elastic-plastic stress analyses of pressure vessels are summarized. Firstly, expressions of load and structural deformation relationship were introduced for thin-walled cylindrical and spherical vessels under internal pressure. Secondly, the plastic instability for thin-walled cylindrical and spherical vessels under internal pressure were analysed. Thirdly, to prevent pressure vessels from local failure, the ductile fracture strain of materials was discussed.

Limiting Plastic Load in a Pressure Vessel with a Branch Pipe under Combined Internal Pressure and Bending Moments

2013 ◽  
Vol 49 (7-8) ◽  
pp. 549-554
Author(s):  
V. N. Skopinskii ◽  
N. A. Berkov ◽  
N. V. Vozhova ◽  
A. B. Smetankin
Keyword(s):  
Internal Pressure ◽  
Pressure Vessel ◽  
Branch Pipe ◽  
Bending Moments

Design for Leakage in Flange Joints Under External Loads

2005 ◽  
Author(s):  
William J. Koves
Keyword(s):  
Internal Pressure ◽  
Analytical Model ◽  
Test Data ◽  
Pressure Vessel ◽  
Research Council ◽  
Bending Moments ◽  
Design Recommendations ◽  
Model Based ◽  
External Loads

This paper uses an analytical model based on the Pressure Vessel Research Council (PVRC) ROTT test gasket constants to compute leakage in gasketed flange joints subjected to internal pressure and external bending moments. The model results are compared with test data and design recommendations are made, consistent with the ASME/PVRC tightness based methodology.

An Analytical Method for Cylindrical Shells With Nozzles Due to Internal Pressure and External Loads—Part II: Design Method

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Ming-De Xue ◽  
Qing-Hai Du ◽  
Keh-Chih Hwang ◽  
Zhi-Hai Xiang
Keyword(s):  
Internal Pressure ◽  
Design Method ◽  
Cylindrical Shells ◽  
Theoretical Method ◽  
Combined Loads ◽  
Stress Components ◽  
Bending Stresses ◽  
External Forces ◽  
External Loads ◽  
Theoretical Stress

A universal design method for pressurized cylindrical shells with attached nozzles subjected to external forces (moments) and internal pressure are presented, based on theoretical stress analysis. The applicable ranges of the presented design methods are extended to ρ0=d/D≤0.9 and λ=d/(DT)1/2≤12. As a first step of design, the required reinforcement thicknesses, both of the main shell and nozzle due to internal pressure, can be determined by the presented theoretical solutions. When the junction is subjected to external nozzle loads, the next step is to determine the absolute values of dimensionless longitudinal and circumferential, normal and shear, membrane and bending stresses in the shell at the junction subjected to internal pressure, and six external nozzle load components by reading out from a number of sets of curves calculated by the present theoretical method. Then the stress components at eight examination points are calculated and superimposed for the combined loads. Finally, the membrane and primary plus secondary stress intensities can be calculated, respectively, to meet the design criteria.

Stress Analysis and Stress Index Development for a Trunnion Pipe Support

1982 ◽  
Vol 104 (2) ◽  
pp. 73-78
Author(s):  
M. H. Sadd ◽  
R. R. Avent
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Stress Analysis ◽  
Wall Thickness ◽  
Pressure Vessel ◽  
Stress Index ◽  
Secondary Stress ◽  
Empirical Formulas ◽  
Stress Indices ◽  
Finite Element Stress Analysis

A finite element stress analysis is presented of a trunnion pipe anchor. The structure is analyzed for the case of internal pressure and various end moment loadings. Stress results were post-processed and decomposed into average and linear varying (through the wall thickness). These decomposed values were then interpreted within the ASME Boiler and Pressure Vessel Code to estimate primary and secondary stress indices. Several computer runs were made for a variety of structural sizes and empirical formulas were developed expressing the stress indices as a function of certain dimensionless ratios.

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